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National and Regional Contests
New Zealand Contests
NZMOC Camp Selection Problems
2018 NZMOC Camp Selection Problems
5
5
Part of
2018 NZMOC Camp Selection Problems
Problems
(1)
abc >= 4038^3 if 1/(a + 2019)+1/(b + 2019)+1/(c + 2019)=1/2019
Source: New Zealand NZMOC Camp Selection Problems 2018 p5
9/19/2021
Let
a
,
b
a, b
a
,
b
and
c
c
c
be positive real numbers satisfying
1
a
+
2019
+
1
b
+
2019
+
1
c
+
2019
=
1
2019
.
\frac{1}{a + 2019}+\frac{1}{b + 2019}+\frac{1}{c + 2019}=\frac{1}{2019}.
a
+
2019
1
+
b
+
2019
1
+
c
+
2019
1
=
2019
1
.
Prove that
a
b
c
≥
403
8
3
abc \ge 4038^3
ab
c
≥
403
8
3
.
algebra
inequalities